Research Questions in Quantitative Political Science

• Normative

  • Focused on subjective, moral questions about the world and how things ought to be.

• Empirical

  • Focused on objective explanation and description, questions about how the world is and why.

\[ \definecolor{treatment}{RGB}{255, 53, 94} \definecolor{treat}{RGB}{253, 91, 120} \definecolor{orange}{RGB}{255, 96, 55} \definecolor{confounders}{RGB}{255, 153, 51} \definecolor{lime}{RGB}{204, 255, 0} \definecolor{resp}{RGB}{102, 255, 102} \definecolor{index}{RGB}{170, 240, 209} \definecolor{untreat}{RGB}{80, 191, 230} \definecolor{pink}{RGB}{255, 110, 255} \definecolor{sample}{RGB}{255, 0, 204} \definecolor{operator}{RGB}{255,255,255} \]

• How should the world look? Asks for a moral judgement

  • Who should be responsible for paying for the consequences of climate change?

  • Should we fire Elon Musk into the Sun?

  • Should women have autonomy over their reproductive choices?

  • Is it fair to forgive student loan debt?

• Normative arguments are common in certain areas of law and philosophy but have no place in this course as they do not lend themselves to scientific answers

• Empirical approaches can be descriptive or causal, quantitative or qualitative, experimental or observational but they all aim to answer some question about how, what, or why the world is.

• Description focuses on observing and measuring the state of the world; it aims to answer questions about who or what in relation to some phenomena (Gerring 2012).

  • What is democracy and how can we operationalize it?

  • Who won the 2020 presidential election election?

• Descriptive approaches tend to lend themselves to dichotomous answers

  • Is country \(A\) more democratic than country \(B\)?

  • Is American democracy in decline?

  • Did Donald Trump lose the 2020 U.S. presidential election?

• Yet, it is necessarily inferior to causal approaches because it cannot answer questions of why or how things happen

• We’ll take a more detailed look at the role of description in quantitative political research when we discuss measurement

• Causal approaches are concerned with explaining why some phenomenon occurs in the world (Samii 2016).

• Contemporary political science is a discipline interested in answering causal questions.

  • Why do poor conservatives tend to vote against their own economic interests?

  • How do gender-inclusive peace processes influence the risk of conflict recurrence?

  • How would the world change if we fired Elon Musk into the Sun?

• Our focus in this class will be primarily on causal questions and entirely on empirical approaches to the study of politics

• Does forgiving student loan debt increase inflation?

  • Imagine student loan debt is forgiven and inflation increases

  • Would this increase have happened if student loan debt had not been forgiven?

• How do gender-inclusive peace processes influence the risk of conflict recurrence?

  • Conflicts that terminate with gender-inclusive peace provisions tend to be less likely to recurr

  • Would conflict have recurred in the abscence of these gender-inclusive peace provisions?

• Causal inference is about counterfactuals

• Imagine a study of \(\color{sample} n\) individuals

  • \(\color{sample} n_{\color{treat} 1}\) are assigned some treatment

  • \(\color{sample} n_{\color{untreat} 0}\) do not receive the treatment

• For each individual \(\color{index} i \color{operator}\in \{1, 2, \dots, \color{sample} n \color{operator}\}\) we observe the outcome \(\color{resp}Y_{\color{index}i}\)

• Treatment status for each individual \(\color{index} i\) \[\color{treatment} X_{\color{index}i} \color{operator} = \begin{cases}\color{treat} 1 \text{ if treated}\\ \color{untreat} 0 \text{ if not treated}\end{cases}\]

• Some set of pre-treatment covariates \(\color{confounders} Z_{\color{index}i}\)

• We want to know the causal effect of \(\color{treatment} X_{\color{index} i}\) on \(\color{resp} Y_{\color{index} i}\)

  • If an individual is treated, \(\color{treatment} X_{\color{index} i} \color{operator} = \color{treat} 1\) and we observe some value of \(\color{resp} Y_{\color{index} i}\)

  • What value of \(\color{resp} Y_{\color{index} i}\) would we have observed if \(\color{treatment} X_{\color{index} i} \color{operator} = \color{untreat} 0\) instead?

• Fundamental Problem of Causal Inference

  • For each individual \(\color{index} i\) we can only observe \(\color{treatment}X_{\color{index} i} \color{operator} = \color{treat}1\) or \(\color{treatment}X_{\color{index} i} \color{operator} = \color{untreat} 0\)

  • Causal inference is a missing data problem

• How do we overcome this problem?

  • We make assumptions to bridge these parallel worlds

• A study of \(\color{sample} n\) billionaires

• For each billionaire \(\color{index} i \color{operator}\in \{1, 2, \dots, \color{sample} n \color{operator}\}\) we observe the state of the world \(\color{resp}Y_{\color{index}i}\) before and after they are assigned to either the treatment or control group

• Treatment status for each billionaire \(\color{index} i\) \[\color{treatment} X_{\color{index}i} \color{operator} = \begin{cases}\color{treat} 1 \text{ if fired into the Sun}\\ \color{untreat} 0 \text{ if not fired into the Sun}\end{cases}\]

• Some set of pre-treatment covariates \(\color{confounders} Z_{\color{index}i}\)

• The causal effect of firing a billionaire into the Sun is

  • \(\color{resp}Y_{\color{index}i}\color{treat}(\text{Fired into the Sun})\color{operator} - \color{resp}Y_{\color{index}i}\color{untreat}(\text{Not fired into the Sun})\)

• For each billionaire \(\color{index} i\) we can either fire them into the Sun or not fire them into the Sun, but it is impossible do both

  • This is the fundamental problem of causal inference

• Also illustrates some practical limitations

  • No IRB would ever approve this study and billionaires are a hard to sample population 😭

  • It is really, really hard to fire subjects into the Sun

  • More efficient to eject them out of the Solar system with a gravity assist from Jupiter instead

• Descriptions of how the world is, correlations, joint distributions, predictions, regression coefficients, odds ratios, probabilities, etc.

  • All of these things may be useful and some may have causal interpretations under specific circumstances

  • They do not, however, in and of themselves capture causal relationships without additional assumptions

• A causal effect is the change we would observe if we manipulated some feature of the world while holding all else constant

  • Sometimes we do not know because we cannot know–there is no magic

• We could just make some claims and use a bunch of weasel words to avoid saying “cause” and “effect” while still heavily implying causality, right?

  • “\(\color{treatment}X\) explains \(\color{resp}Y\)”

  • “\(\color{treatment}X\) has an impact on \(\color{resp}Y\)”

  • “People who do \(\color{treatment}X\) are more likely to experience \(\color{resp}Y\)”

• Lots of people still do this!

  • Makes it hard to distinguish between what is real and what is not, results in the proliferation of pseudo-facts (Samii 2016)

  • Important to be explicit about our assumptions, intentions, and goals

• Difference between normative and empirical approaches in political science

  • Distinction between descriptive questions and causal questions

• Counterfactuals and the Fundamental Problem of Causal Inference

• What causal inference is and what it is not

• We will spend the rest of the semester building on this foundation

• Read the installation instructions on Canvas under the module for Week I

• Easiest way to avoid headaches involving file paths is for you to clone the course’s repository from github

  • Either download a zip file of the current version and extract that somewhere on your computer

  • Or you can install git which integrates with RStudio

    • Happy Git and GitHub for the useR is a free online book on getting started with git in RStudio

    • This approach let’s you pull updates from the course repo directly from RStudio

• This will ensure your relative file paths match mine and will make it easier for me to help you

• Project-Oriented Workflow

  • Work in RStudio projects

    • Helps you keep things organized in appropriate subfolders

    • All file paths are relative to the .Rproj file’s location

  • Write code in scripts

    • Helps you keep track of and structure your data, analysis, etc.

    • Comment your code

    • Use seperate scripts for each part of your analysis, problem sets, etc.

• We’ll talk more about Quarto and dynamically reproducible documents next week